{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "134e7f9d",
   "metadata": {},
   "source": [
    "# API 2: Plotting"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2571d531",
   "metadata": {},
   "source": [
    "Initialize KAN and create dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "2075ef56",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "cuda\n",
      "checkpoint directory created: ./model\n",
      "saving model version 0.0\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(torch.Size([1000, 2]), torch.Size([1000, 1]))"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from kan import *\n",
    "\n",
    "device = torch.device('cuda' if torch.cuda.is_available() else 'cpu')\n",
    "print(device)\n",
    "\n",
    "# create a KAN: 2D inputs, 1D output, and 5 hidden neurons. cubic spline (k=3), 5 grid intervals (grid=5).\n",
    "model = KAN(width=[2,5,1], grid=3, k=3, seed=1, device=device)\n",
    "\n",
    "# create dataset f(x,y) = exp(sin(pi*x)+y^2)\n",
    "f = lambda x: torch.exp(torch.sin(torch.pi*x[:,[0]]) + x[:,[1]]**2)\n",
    "dataset = create_dataset(f, n_var=2, device=device)\n",
    "dataset['train_input'].shape, dataset['train_label'].shape"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8c6add1d",
   "metadata": {},
   "source": [
    "Plot KAN at initialization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "ac76f858",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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v3LkjzmyEeES4/ObCwsJ48OBBDh48mJ6enjQ1NSUAZsqUiQ0bNuScOXN448YNg4RJHI1Gw4MHD7J06dIEwBIlSnDv3r2yH7zkDJc4r169Yv/+/ZkmTRra2tpyyJAhfPfunUFrCA0N5Z49e9i/f38WL15cGzaOjo5s1qwZFy5cyH///Vf270uQl+gW+82EhYXh1KlT2m6uCxcuQKVSIXPmzPGe9s6XL5/BuzxI4uDBgxg9ejTOnDmDkiVLYuTIkahWrZpRdL/I0S32I2/evIGfnx/mzp0LSZLQo0cP9OvXD/b29gav5fPnzwgKCtJ2o128eBFqtRpZsmSJ142WJ08eo/geBcMQ4ZLKxe34cWFijDs+SRw4cACjR4/G2bNn4enpiZEjR6JKlSpGdTAypnCJ8+7dO/j5+WHOnDkgib/++gv9+/dHpkyZZKvp6x8w58+fh1qt1v6Aidvm5PgBIxiQjGdNgh78rMuiefPmRtVlodFouGfPHpYoUYIAWLp0aR46dMgoavseY+gW+5G3b99y8ODBtLGxYZo0aThgwAC+fv1a7rJIJrzr1Vi/dyFpxJlLChcaGorAwEDtr8TLly9Do9EgW7Zs2hF0vby8kCtXLqP5lUgSe/bswZgxY3DhwgWULVsWI0eORKVKlYymxu8xxjOXr71//x4zZszArFmzoFar0a1bNwwYMMCoRlCOiIjA6dOntd1o586dg1KphL29fbwzmwIFCujtDkRB/0S4pDAp+TZRkti9ezdGjx6NS5cuoXz58hg5ciS8vb2NrtbvSQnhEufDhw/w9/fHzJkzoVQq0bVrVwwcONAoR042htvdBT2Q8axJSIAfPeDm7OzMNm3apIgH3DQaDbdv386iRYsSAL28vHj8+HG5y0o0Y+4W+5EPHz5wxIgRTJcuHS0tLdmnTx++ePFC7rJ+KjIykseOHdM+qGtubv7dB3UNeQejkHjizMXIvHv3DidPntT+irt27RoAwMXFJd7dXDlz5pS30ATQaDTYsWMHxowZg6tXr8Lb21s7sVZKlJLOXL4WGhqKmTNnwt/fH9HR0ejcuTMGDRoER0dHuUv7paioKJw9e1Z7th4cHIyYmBjY2dmhfPny2v2icOHCCZ6nRzAAudPtd5eQQQUfPXokd5mJolaruWXLFu24VZUqVeLJkyflLivZUuKZy9dCQ0M5ZswY2tnZ0cLCgj169Ehxw/H/aHDUdOnS6WVwVCFpRLgY2KtXr7hx48bvDofesWPHFD0culqt5qZNm7QhWblyZQYGBspdls6khnCJExoayrFjxzJ9+vQ0NzfnX3/9xadPn8pdVpJER0czMDCQY8eOZeXKleNN61CjRg1OmTKFZ8+eFWFjYCJc9Ozly5epfiInlUrFDRs2sECBAgTAKlWq8NSpU3KXpXOpKVzifPr0iePHj2eGDBlobm7Obt26pdgfN3F+NCGdra2tTiakExJGhIuO/U5T0KpUKq5fv14bmtWqVePp06flLktvUmO4xPn8+TMnTpzIjBkz0szMjF27dk01c7zExMToZSpt4edEuCTTs2fPuGbNGnbq1Inu7u7aMMmXLx+7devGDRs28OXLl3KXqVMqlYpr165l3rx5CYDVq1fnmTNn5C5L71JzuMQJCwvjpEmTaG9vTzMzM3bu3DnFXfP7ldjYWJ45c4aTJk1i9erVaWNjow0bHx8fjh8/nkFBQYyJiZG71BRNhEsiPXnyhKtXr2aHDh2YK1cubZgUKFCA3bt356ZNm/jq1Su5y9QLpVLJ1atXa8/IfH19efbsWbnLMpjfIVzihIWFccqUKcyUKRNNTU3ZsWNHPnjwQO6y9EKpVPLs2bOcMmUKa9SoQVtbWwKglZUVK1euzLFjxzIwMJDR0dFyl5qiiHD5hcePH3PlypVs164dXV1dtWFSsGBB9ujRg5s3bzaaYTb0RalUctWqVdozs5o1a/LcuXNyl2Vwv1O4xAkPD+fUqVPp4OBAU1NTdujQgffv35e7LL1SKpU8f/48p06dypo1azJt2rQEQEtLS1asWJFjxoxhQECACJtfEOHylYcPH3L58uVs27Ytc+bMqQ0TDw8P9urVi1u3buXbt2/lLtMglEolV6xYoT1Dq127Ni9cuCB3WbL5HcMlTkREBP38/Jg5c2aamJiwXbt2vHfvntxlGYRKpeLFixfp5+fHWrVq0c7OThs2FSpU4KhRo3j8+HFGRUXJXapR+a3DRaPR8P79+1y2bBlbt27NHDlyEAAlSWKRIkXYu3dvbt++3eDzZcgtNjaWy5Yto5ubGwGwbt26vHTpktxlye53Dpc4ERERnDFjBrNkyUITExO2adOGd+/elbssg1KpVLx06RJnzJjBOnXqMH369ARACwsLenl5ccSIETx27BgjIyPlLlVWv1W4aDQa3rt3j0uWLGGrVq3o5OSkDZOiRYuyb9++3LlzJz98+CB3qbKIjY3l0qVLtd1/9erV4+XLl+Uuy2iIcPl/kZGR9Pf3Z9asWalQKNi6dWveuXNH7rJkoVareeXKFfr7+7NevXrMkCEDAdDc3JzlypXj8OHDeeTIEUZERMhdqkGl6nDRaDS8c+cOFy1axBYtWjBbtmwEQIVCwT/++IN///03d+3a9duGSZzY2FguXryYLi4uBMAGDRrw6tWrcpdldES4fCsqKoqzZs2io6MjFQoFW7Zsydu3b8tdlqzUajWvXbvGWbNmsX79+rS3tycAmpmZsUyZMhw6dCgPHTrE8PBwuUvVq1QVLhqNhrdv3+bChQvZrFkzOjo6asOkRIkS7N+/P/fs2cPQ0FC5SzUKMTExXLhwobY7sFGjRrx27ZrcZRktES4/FhUVxTlz5jBbtmxUKBRs3rw5b926JXdZRkGtVvP69eucM2cOGzZsyEyZMhEATU1NWbp0aQ4ePJgHDx5kWFiY3KXqVIoOF41Gw1u3bnH+/Pls2rQps2TJQgA0MTHhn3/+yYEDB3Lv3r389OmT3KUalZiYGC5YsIDOzs6UJImNGzfm9evX5S7L6Ilw+bXo6GjOnTuX2bNnpyRJbNasGW/evCl3WUZFo9EwJCSEc+fOZePGjeng4KANm1KlSnHQoEHcv38/P3/+LHepyZKiwyU2NpbW1tY0MTFJVV+Kvo0dO5aSJLFp06YMCQmRu5wUQ4RLwkVHR3P+/Pl0cnJi2rRpU30XUHJ8+SO5SZMm2h/JkyZNkru0ZDG6Ife3bduGT58+IV26dHqdQEqj0aBBgwZ6W74hbdu27YdtRRLR0dGwsrJK9npSU5sBSdvWNBpNoiesSk3t9uW2RhJKpRIqlQomJiYwNzfX2T6bmtoM+PE+GhsbCwAwNzfXyXqMqd1M5S7ga8HBwTh27Bjy5MmDdu3aoWzZsjAzM9P5egYNGmQ0X0JynTlzBhMmTPjmv7948QKDBw/GrVu30LBhQwwcODBZ6/nnn39STZsB/7Xb0aNH4erqitq1a8PHxwcZM2b8aVDHScxBNDW1W3BwMGrXro3Tp0/j4sWLePr0KaKiomBhYQE3NzdUq1YNNWvWRNq0aZO1ntS0fwLf7qMksX79eixYsAAKhQKjR4/WyTxHxrStGV24AMDcuXOxceNGdOzYEbly5cKwYcPg5eUlpjj9CVPT//8qSeL8+fNo2LAhypYti9GjR2v/d/ny5WWs0vjMnTsX+/btg7+/P8aMGYMWLVqgc+fOyJo1a4qYelkOffv2Rfbs2VGiRAk0bNgQadOmRXh4OK5evQo/Pz9MnjwZEydORK1atUQbfiFuHyWJYcOGYeHChZg0aRI+f/6MmjVr4unTp7C3t5e5St0xynApVaoUSpYsiQEDBmDhwoVo2rQpatSogcmTJ8PBwUHu8owaSaxbtw7du3fHoEGDMGjQIJiYmGDu3LmoU6cOPnz4kOAdnmSqPzjEbWuDBg3CyZMn4e/vj+XLl6NPnz7o2rWrTroTU5sjR47A1tYWCoUi3vbRoEEDDBo0CKtXr0a7du3Qvn17TJo0ScwO+QWSGD9+PObPn49Tp04hb968AIDz58+jRo0aOHfunMwV6o7RngpIkgRHR0eMGjUKgYGBePPmDUqVKoWAgAAY2WUio0ASHz9+RJ8+fdC7d2+sWLECgwcP1u7YHTp0wKdPnxAVFZWgZZ06dQojRozAsmXLcPv2bVy4cEHfH0E2kiTB2toa1atXx549ezB79mwsW7YMlStXxrVr18T29hU7OzuYmJh888NDkiTY2Niga9euOHnyJLZu3YqWLVtCpVLJVKlxIYl58+Zh0qRJCAgIQL58+SBJEiRJwvLly3HhwgXExMTIXabOGG24xJEkCblz58bOnTvRo0cP1KpVCwsXLhQ7/FdmzpwJT09PXLlyBUFBQahbt268nV+SJOTIkQOTJk365bKuX7+OKlWq4M2bN1i5ciVq1aqFDh066LN8o2FmZobatWvj1KlTKF26NLy9vbF06VKxvSWCJEkoUKAAzpw5g8uXL6NFixbQaDRylyU7Pz8/DB48GAcPHkShQoXi/c3S0hKurq4YPXq0TNXpntGHSxxTU1P07dsX27Ztw+DBgzFixAixw3/h5s2bGDp0KA4ePIi8efN+tztr1qxZ8PPz++lySMLHxwcjRozAggULcOjQIRw9ehTHjh3TV+lGKW3atJgyZQpWrVqFIUOGoHfv3lAqlXKXlaI4ODggKCgIp06dQu/evX/7/TUiIgJHjhxB6dKlv/v3devWYdq0aQauSn+M8prLj0iShEqVKiEwMBCVKlVCeHg4pk+fnuqvCyTE/Pnzf9m3XaNGDURFRf30WsqnT5/w9u1bDBgwAJIkwcLCAs7Ozvoo2ehJkoQaNWrg9OnTqF27Nho0aICNGzeK6zCJYG9vj+DgYOTLlw8FChRAly5dftv9dcSIET/97CVKlIBKpUJsbKzObk2WU4o5c4kjSRIKFiyI06dPY+3atRg4cOBv/4sIQIIumsa9Ju7e+u/p378/ihQpIu7M+x9JkpArVy4EBQXh7du3qFatGiIjI+UuK0VxcnLCoUOH0KNHD1y6dEnucmTzq1CVJAn29vZYtGiRgSrSrxR7BHFzc0NwcDCWLFmCcePGiYBJIGtra+zevfuHf1+1ahUWL15swIpShgwZMuDo0aOQJAk+Pj6Ijo6Wu6QUxdPTE9OmTUPFihURHh4udzlGa/r06Rg2bJjcZehEig0X4L+ACQwMxMSJE8VF1wRq0aIFxo4d+92/kYRKpUKxYsUMXFXKkCZNGuzfvx8k4evrK+6CSgRJktC7d2+ULl0aVatWFfvqDzRt2hSfP39OFe2TosMFAAoWLIj9+/eje/fuOHr0qNzlGL3+/fvjxo0b3/3by5cvASTu6fPfjZWVFQ4fPoyXL1+iVatWqeIgYCiSJGH79u0ICQnBrFmz5C7HKJmamkKSJDx79kzuUpItxYcLAJQvXx7Lli1DrVq1cPfuXbnLMWpubm7gfwOWfvO3iRMnIn/+/DJUlbJYW1sjMDAQx44dw/Dhw0XAJIKlpSWOHj2Kv//+G8+fP5e7HKNUvnx59O7dW+4yki1F3S32I5IkoUWLFrh58ybKli2Lu3fvJntso9Qq7qxEpVJ9M2bbihUrsGLFChmqSnkyZsyIwMBAeHh4oEiRImjYsKHcJaUYxYoVQ5cuXVChQgXcuXNHnCl/Ze7cufDw8JC7jGRLFWcuwH8HzfHjx6NkyZKoWLEi1Gq13CUZLXNzc5w6deqb/x4REYFatWrJUFHKlDt3bmzduhUtWrTA/fv35S4nxZAkCbNnz8a7d+8wZ84cucsxOvny5YNGo0nxD56mmnAB/ttot2zZgs+fP6NDhw6iu+IHKleu/M0oynEbsj5GoE7NatSogX79+qFcuXKpaugOfTMxMcGhQ4fQp08fcffYV+KeLzt+/HiC3xMREYETJ07or6gkSFXhAvz3qzwoKAhbt27F3LlzRcB8x9ChQ7/ZEC9evKi9mCgknCRJGDduHJycnNCkSROxvSVC8eLFUblyZdSuXVu021d69eqFrl27Jui1JFGrVi1MnTpVz1UlTqoLF+C/YSeOHj2Kvn37IigoSO5yjM6ff/4JlUoVb4ceOnQofHx8ZKwq5VIoFDh8+DAOHz6MNWvWyF1OiiFJErZt24aAgACEhITIXY5RGTZsGO7fv//L0CWJyZMn4+rVq9i8ebOBqkuYVBkuwH9DKcybNw/VqlXDixcv5C7HqMQ9ff/ldanjx49j/PjxcpWU4qVNmxa7d+9Ghw4d8PbtW7nLSTGsra0xZswY+Pj4iLOXL9jY2AAAXr9+/cPXkMT27dsxatQoHD9+HGnSpDFUeQmSasNFkiR07NgRrVq1QpkyZcQT1V+I69ONG4ySJNRqdaq4Q0VO3t7eaNGiBby9vcWBMhEGDx6MT58+YceOHXKXYjTixlHs2LHjD18TEBCA5s2bY+PGjUa576bacAH++4Lmzp0LR0dH1KpVK8XffaFLLVu2xKBBgwAAb968AQAxnlgySZKExYsX4+XLl/D395e7nBRDoVBg3bp1aN68uQjlL6xYsUI7IsTXrl+/Dl9fX8yZMwe1a9eWobpfS/VHk7i7Um7fvi2G/f7C2LFjcfXqVZDEgAEDUKJECblLShVMTU1x5MgRDBgwQHSPJUKdOnVgZWWFBQsWyF2K0XB0dISZmdk3N9+8ePECXl5eGDJkCDp06GC0N+Gk+nAB/uvXPXXqFJYvXy7uIPufzJkzAwDCwsKwfv16LF26VOaKUo8iRYqgRYsWqFy5stjWEkiSJOzatQu9evUSPQz/E/c8UIMGDbTj2L169QplypRBw4YNMWTIEKMNFuA3CRcAcHZ21g47sX//frnLkZ0kSfD29kbjxo21MwcKuiFJEpYsWYL79+9j/fr1cpeTYpQpUwZp06bFvHnz5C7FaHTs2BEODg5o3rw5li9fDk9PT5QtWxYLFiww6mABjHT4F31dfC9cuDCWLl2KxYsXw9XVVS/rkEtS2mz9+vWoV68eli9f/ts+AKjPGz02bNiApUuXws3NTW/rkIM+22zz5s3w9/eHu7u73tYhl6S2W9yP4qVLl6Jnz57o2rXrT+dkMhYSjey8fd++fXofylylUsHCwgK+vr56XY+hJKfNlEplgp/KNzExSTVtBhhmW1Or1TA3N0817SbaLGmS225x02H8al81pn3U6MLFkOUY+2llQok2SxrRbokn2ixpfsd2M7prLpIkJepfVFQULl++jKioqES/N7UQbZY0ot0ST7RZ0vyO7WZ04ZJYt2/fxh9//IHbt2/LXUqKIdosaUS7JZ5os6RJDe2W4sNFEARBMD4iXARBEASdE+EiCIIg6JwIF0EQBEHnRLgIgiAIOifCRRAEQdA5ES6CIAiCzolwEQRBEHROhIsgCIKgcyJcBEEQBJ0T4SIIgiDonAgXQRAEQedEuAiCIAg6J8JFEARB0DkRLoIgCILOiXARBEEQdE6EiyAIgqBzIlwEQRAEnRPhIgiCIOicCBdBEARB50S4CIIgCDonwkUQBEHQOREugiAIgs6JcBEEQRB0ToSLIAiCoHMiXARBEASdE+EiCIIg6JwIF0EQBEHnRLgIgiAIOpeiw4UkPn78CAD4+PEjSMpckfETbZY0ot0ST7RZ0qSadmMK9PHjR/r7+9PNzY0AtP/c3Nzo7+/Pjx8/yl2i0RFtljSi3RJPtFnSpLZ2S3HhcuDAAVpbW1OSJEqSFO9LiPtv1tbWPHDggNylGg3RZkkj2i3xRJslTWpstxQVLgcOHKCJiQkVCkW8xv/6n0KhoImJSYr6IvRFtFnSiHZLPNFmSZNa200iU0aHXmhoKLJnz46oqChoNJpfvl6hUMDKygrPnj2DnZ2d/gs0QqLNkka0W+KJNkua1NxuKeaC/sqVKxEZGZmgLwAANBoNIiMjsWrVKj1XZrxEmyWNaLfEE22WNKm53VLEmQtJuLu748GDB4m6c0KSJLi6uuLu3buQJEmPFRof0WZJI9ot8USbJU1qb7cUES7v3r1DpkyZkvX+jBkz6rAi4yfaLGlEuyWeaLOkSe3tliK6xcLDw5P1/rCwMB1VknKINksa0W6JJ9osaVJ7u6WIcLGxsUnW+21tbXVUScoh2ixpRLslnmizpEnt7ZYiwiVjxoxwc3NLdP+iJElwc3NDhgwZ9FSZ8RJtljSi3RJPtFnSpPZ2SxHhIkkSevbsmaT39urVy6gveumLaLOkEe2WeKLNkia1t1uKuKAPpO77wfVFtFnSiHZLPNFmSZOa2y1FnLkAgJ2dHbZu3QpJkqBQ/LxshUIBSZKwbds2o/8C9Em0WdKIdks80WZJk6rbzdBDAiRXQsfgOXjwoNylGg3RZkkj2i3xRJslTWpstxQXLuR/o4fOnDnzu6OHzpw5k6GhoXKXaHREmyWNaLfEE22WNKmt3VJkuMTRaDQ8evQoAfDo0aPUaDRyl2T0RJsljWi3xBNtljSppd1SzDWX75EkSdv3aGdnZ/R3TxgD0WZJI9ot8USbJU1qabcUHS6CIAiCcRLhIgiCIOicCBdBEARB50S4CIIgCDonwkUQBEHQOREugiAIgs6JcBEEQRB0ToSLIAiCoHMiXARBEASdE+EiCIIg6JwIF0EQBEHnRLgIgiAIOifCRRAEQdA5ES6CIAiCzolwEQRBEHROhIsgCIKgcyk2XMLDw3Hnzh1cv34dAPDq1SvExsbKXJXxCw8Px+PHjwEAt27dwtOnT0W7/YJSqcTz589x69YtAMD9+/fx4cMHaDQamSszbmJbS7zUdFyTSFLuIhLjwYMHWLJkCXbt2oWnT59CqVQiJiYGadOmRdGiRdGmTRvUr18ftra2cpdqVL5st8ePHyMqKgrm5uawtrZGoUKFRLt9R2hoKLZu3Yq1a9ciJCQEYWFhiI2NhaWlJTJlyoRy5cqhQ4cOKFOmDExNTeUu12iIbS3xUuNxLcWEi1qtxvr16zFkyBBERUWhevXq8PHxgbOzMzQaDe7du4f9+/fj+PHjKFasGGbPno38+fPLXbbsRLslTXBwMPr27Ytr166hRIkS8PX1hYeHB2xsbBAaGoqLFy9i9+7duHfvHpo0aYJx48YhU6ZMcpctK7GtJV6qbjOmAGq1mnPnzqW1tTWrV6/Oq1evUqVS8fTp05w5cyZnzpzJW7duMTY2lgEBASxevDjz5MnD69evy126rES7Jc3BgweZNWtWuru7c8uWLYyMjGRoaCgXLFjAmTNncvny5YyKiuLnz5+5aNEiOjo60sfHh69evZK7dNmIbS3xUnubpYhwOX78OO3s7NiwYUN++PCBGo2GJDls2DACIACuXr2aJKnRaPj48WOWLl2aZcuW5cePH2WsXF6i3RLv33//pYuLCwsWLMgbN25o2+z+/ftMly4dAdDFxYUfPnwg+V+7nTx5ktmzZ2fLli0ZHR0tZ/myEdta4qX2NjP6C/pRUVEYM2YMMmfOjBkzZsDOzg6SJP3w9ZIkwcnJCbNnz8adO3ewZs0aA1ZrPES7JZ5arcaECRPw8eNHzJkzB/nz5/9pmwH/tVvZsmUxZcoU7Ny5EwcOHDBQtcZDbGuJ9zu0mdGHy8WLF3HmzBl0794d2bJl++XODvz3RRQpUgSNGzfGihUrEBkZaYBKjYtot8S7d+8edu/ejfr166Ns2bIJajPgv3arW7cuSpUqhcWLF0OlUum5UuMitrXE+x3azOhvcTlx4gQsLCxQuXJl3Lp1K96O+/r1a+3/fvLkCa5du6b9/3Z2dqhbty7WrFmDR48epZyLYDoi2i3xTp8+jfDwcDRo0ACPHj1CRESE9m/Pnj2DWq0GAMTGxiIkJARp06bV/t3R0RH169fHqFGj8OrVK2TPnt3g9ctFbGuJ91u0mdz9cr/SsmVL5s6dm3fu3KGzszMtLS21/0xNTbV9k2ZmZvH+1q5dOz58+JD29vbcv3+/3B/D4ES7Jd7AgQNpZ2fHW7dusVKlSvHaxcLCQttmkiTF+5uVlRXnzZvHwMBA2tra8uzZs3J/FIMS21ri/Q5tZtRnLiQRHR0NCwsLmJiYIDo6GtHR0d99rVKphFKp1P7/2NhYmJuba9/3OxHtljRRUVEwNTWFhYUFYmJifvj549r3SyqVClZWViCJmJgYQ5RrFMS2lni/S5sZdbhIkgR7e3ucO3cOarUa3t7eCA0N1f797t27ePDgAQCgUKFCcHR01P7Nw8MDoaGhCAsLw5AhQ3DixAl4enqiVKlScHZ2TnB/ekqki3aLiorSdgP9LhwcHBAVFYXQ0FCULFkS1tbW2r9FRUXh9OnT2hApXbq09sFJSZLg7OyMN2/eQKFQIH369HJ9BINSKpUIDg7G/fv3ERoamuRtLSYmBhkyZDB0+QYVFRWFS5cuITg4GGfOnMH+/fuRIUOG1N1mcp42JcTixYtpZWXFkydPUqVSxfs3ZMgQ7enjypUr4/1NrVZzxYoVTJs2LevVq0dXV1fta7Nmzcp69epxypQpPHnyJCMjI+X+mDqX3HaTJIkA6OHhwUGDBvH48eOMjY2V+2PpzcuXL9mmTRtKksQFCxZ802Z37tzR3oqcM2dOvnv37pt2GzRoEJ2cnPj+/Xu5P47ePH36lIsXL2b9+vWZNm1aAqCNjQ0tLCySvK1lyZKFz549k/uj6YxGo+GDBw+4bt069uzZkyVKlKCZmRkBME2aNPTy8mK1atVoaWmZqtvMqM9cAKBixYqwtbXFypUr4enpGW+YDYVCEe9/m5iYaP9/ZGQkVq1ahSpVqmDDhg0wMTHBmzdvcObMGZw5cwbBwcEYNWoUIiMjYWpqisKFC8PT01N7duPi4pKiz268vb1hbm6e5HarVasWGjdujEOHDmH58uWYPHkybG1tUblyZVSrVg3Vq1eHk5OTQT+TrqnVahw+fFg77IaJiQnSpk2LlStXolmzZvEu2H/ZRpIkxWs3knjx4gU2b96Mt2/fonLlymjdujWaNWuGzJkzG/xz6VJsbCyCgoJw4MAB7N+/Hzdu3IBCoUCpUqXQv39/VK9eHXZ2dihTpkySt7WyZcsiS5YsBv1cuhQREYGLFy9qz0qCg4O1F+Vz5coFT09PtG3bFp6enihUqBBMTU3x4MEDeHp6pu42kzvdfkWtVrNv3760tbXlnj17tA8akd9/2CjuPXPnzmX69OkZEBDww2UrlUpevnyZ8+fPZ+vWrenu7q5dnoODA2vXrs2JEyfy+PHjDA8P1+vn1KUXL16wefPmTJMmDW1sbJLdbmq1mhcuXOC4ceNYpkwZKhQKAmCBAgXYr18/HjlyJEU9PPjs2TOOHTuWOXPmpCRJ9PDw4OzZs/nhwwfOmTOHFhYWHDt2LJVKpfY9P3qIkiSjoqLYpUsXOjo6cvPmzezRowezZ8/OzJkzs3Xr1jxy5AhVKpUcHzVJHj16xPnz57NOnTq0sbEhAGbOnJlt2rThhg0bvjkzS84+ampqysGDB8d7jzHTaDS8e/cuV69eze7du7NYsWI0MTHRnsFVrFiRQ4YM4e7du/n27dsfLkefxzVjYfThQv7XZVGiRAk6OTnxyJEjVKvVJMkRI0bQ1NSUZmZmXLNmDTUaDZVKJVevXk17e3sOGTIk0Tv1u3fvuGfPHg4bNoyVKlWira0tAdDExIRFihRht27duHLlSt65c8fodgiNRsP169fT3d2dHh4eXLdunV7a7cOHD9y4cSPbtWvHrFmzEgCtra1Zq1Ytzps3jw8fPjTQJ044lUrFPXv2sE6dOjQ1NaW1tTU7dOjA4ODgeN9jeHg4GzduTBsbG/r5+TEyMpIajYb3799nxowZaWpqyly5cmmfqP706RMHDhzIdOnScdmyZdrlhIaGcsmSJSxfvjzt7e1ZpEgRTps2jS9evJDj4/9UdHQ0Dx06xL59+zJfvnza7b1cuXIcP348L126pN12fiSp+2jBggUJgDVq1DDKbp6wsDAePXqU48ePZ82aNWlvb6898OfJk4dt27blggULtEO3JIYhj2tySBHhQpIhISEsVqwYM2TIwKFDh/LevXu8c+cOT5w4wRMnTvDx48e8du0au3btynTp0vGvv/5iREREsterUql47do1Llq0iO3atdPufACYMWNG+vr6cuzYsTxy5Ag/ffqkg0+aNM+fP2ezZs2YOXNm9uzZk6GhoST1324ajYaXL1/mxIkTWb58ee2vuDx58rBPnz48ePAgo6Ki9PWxf+nJkyccNWoUnZ2dKUkSixYtynnz5mnb53vevHnDRo0a0crKinXr1mVAQADfvHnDwMBABgQEMDg4mG/fvuXevXvp7e3N9OnTc/bs2d/d4TUaDS9evMjevXvTycmJDg4ObNGiBQ8ePBjvzMjQ7t+/zzlz5tDX15dp0qQhADo6OrJDhw7cvHlzkoYXSeq2tmvXLmbNmlUb0HL9aNNoNLx9+zaXL1/OLl260MPDQ3uWnjZtWvr4+HDEiBHct2+fzq6rJbTNOnfurNPjmiGkmHAh/7uYGPfr0d7enuXLl2eLFi3YtGlTlipViunTp2euXLm4ePFivXbTfPjwgQcOHODIkSNZtWpVbXeJJEksVKgQO3XqxGXLlvHmzZu//MWXXBqNhmvWrGGuXLlYpEgRHj58+JvXPHv2jF26dKGdnZ3e2y00NJRbt25lx44dmS1bNgKglZUVa9SowdmzZ/Pu3bvJWn5CKJVK7ty5kzVr1qSJiQltbGzYuXNnnj9/PsEHrvDwcM6YMYMuLi5MkyYNCxYsyHr16rF169asVasWc+fOTRsbG3p5efHYsWMJ+p4/f/7M5cuX09vbm/b29vTw8OCkSZP49OnT5H7kX4qMjOT+/fvZq1cvbfevqakpK1SowMmTJ/Pq1as6OagndVv78OED27ZtSwCsWrUqnzx5kuxafiU0NJSHDh3i6NGjWb16daZPn167HxcoUIAdOnTgkiVLeOPGDb3ux79qMzs7OwJgjx49UlT3c4oZch8Adu7cibp162LZsmV48+YNzp07hzdv3sDMzAwuLi7w9vZGlSpV4ODgYNC6NBoN/v3333gX9EJCQkASdnZ2KFWqFEqVKgVPT0/8+eefsLOz08l6nz9/jr///hsBAQFo1qwZRo0ahXTp0n33tWq1Grdu3cLevXsN1m4kERISgv3792P//v0ICgqCUqlErly5UL16dVSvXh1eXl5IkyaNTtb36NEjLFu2DMuWLcOLFy9QvHhxdOzYEc2aNUvyPBivXr3C0aNHERAQgAcPHiA6Ohrp06dHwYIFUaVKFZQsWTJJ9V+9ehWrVq3C1q1bERkZiUqVKqFVq1bw8fGBmZlZkmr9EkntcO379+/HiRMnEB0dDScnJ23bV6xYMd5NC7qSnG1t//796NSpEz5//gw/Pz907NhRJzfWaDQa3L59O94+evPmTZBE+vTpv9lHf7Qf6cvP2qxChQqYN28eYmNjceHChZRzo5GcyZYYGo2GRYoUYYUKFeL9N6VSaZT9j58+feLhw4c5ZswY1qhRgxkyZNB2p+XPn5/t27fn4sWLef369UT/KtJoNFy5ciVdXV1ZpEgRHj16NNHvl6PdPn/+zB07drBLly50dnYmAFpaWrJq1aqcMWMGb9++nehfz7Gxsdy6dSurV69OhULBtGnTslu3brx48aLO61epVFQqlTr9FRseHs7Vq1fTx8eH9vb2LFCgAMePH8/Hjx8naVl79uzhX3/9pb313tzcnJUqVeK0adMYEhJi8C6npGxroaGh7NChAwHQx8eHjx49SvR6P3z4wP3793PEiBGsUqWKtndBoVDQw8ODnTt35vLly3nr1i299y4k1vfa7Pjx4wTAHTt2yFhZ4qSYcNm2bRsB8MSJE3KXkiQajYb//vsvV6xYwa5du7Jw4cLx+nMrV67M4cOHc+/evT/tz338+DEbNGjAzJkzs3///vz8+bMBP4XuaDQa3rx5k35+fvTx8aG5ubn2Tqxu3bpx165dP71D7/79+xwyZAizZMlCSZJYqlQpLl26lGFhYQb8FLp1/fp1Dhw4kC4uLsyUKRMbNWrE3bt3//D5oq/bMG6Impw5c2rbMCW3x4EDB+jk5EQbGxvOnz//hyGgUql49epVLly4kG3btmXevHnjXRetWbMmx40bx6NHj6bY/YUkK1SowCJFihjdjUQ/kiLCRa1W08PDg97e3nKXolNhYWE8duwYJ0yYwFq1asW7EyV37txs06YN58+fzytXrjAmJobLli2ji4sLixUrlmJD9kfCw8O5e/fun/7qjo6O5qZNm+jj40NJkmhnZ8eePXvy6tWrcpevUxEREVy3bh2rVatGe3t75suXj2PHjuXDhw8ZFhbGHTt2sGvXrsyRIwcB0MLCIllnf8bs06dP7Ny5MwHQ29ubDx484Nu3b7l7924OHTqUFStW1N4ubWJiwqJFi7J79+5ctWoV7969m6ra4sSJEwTAbdu2yV1KgqSIay5bt25Fw4YNcfLkSZQrV07ucvSGJB48eKDtEz5z5gyuXLkCtVoNExMTKBQK/PHHH+jbty+8vb1T7bS6JHH37l3tg3vHjx9HTEwMFAoFNBoN8ubNi969e6N169Y6u15jrG7evInp06dj+/btCAsLg0qlAkm4ubmhRo0aqFatGipUqJBq20GlUuH69etYsWIFli5disjISMQdshwcHOI9+Fy8ePF4Q/akRhUrVsT79+9x+fLleA9bGiOjDxeNRoMiRYrAwcEBR44ckbscg9JoNJg/fz7GjRsHU1NTuLq64s6dO3j16hUAwM3NTbtjxT39q4uLwcYgJiYG27dvx+LFi3Hs2DHY2NggV65c+PjxIx4/fgxTU1OULVtWe3G6YMGCKedC5y98/vwZR44cwf79+3HgwAE8e/YMlpaWyJs3L5RKJV68eAEHBwc0bdoUrVq1gpubm9wl68zr16/jjaJx/vx57SgahQoV0oZNyZIlsWbNGuTKlUvukg0qMDAQ5cuXx9atW1G/fn25y/k5+U6aEmbz5s0EwKCgILlLMaj79++zdu3azJw5MwcPHqy9/qDRaPjw4UOuX7+evXr14p9//qkdt8jKyorly5fnwIEDuX37dr58+VLmT5F4t27dYr9+/Whvb09Jkujl5cU1a9bEG//t3r172mc0rKysCIDZsmVjhw4duGXLlp8+w2KMNBoNr1y5on1WKG7I9S+fFfry89++fZtDhw6lu7s77e3tWadOHW7ZsiVF3aZK/nczxvnz5zlr1iw2b96cLi4u8cb/q1+/PqdOncrAwMB4n//YsWN0cXGhlZUV/f39je6CvL5VqlSJhQoVMvrPbdTholarWbBgQfr4+MhdisGoVCouWLCAOXLkYMmSJXn69OlfvicqKoqnTp3itGnT2LBhQ+3zJfjfxd2mTZty5syZPHv2LGNiYgzwKRInMjKSq1evppeXFyVJor29Pfv168dbt2798r1RUVE/fLp8woQJvHTpklH2u3/8+JGbNm364SgHDx48+OUyoqOjuWXLFtauXZv29vZ0d3fnsGHD+O+//xrgEyTe8+fPuXXrVvbv359ly5alpaWl9tpaqVKl2KdPH27cuJGPHz/+5XcWFhbGnj17EgDLli3LO3fuGOhTyC8oKIgAuHnzZrlL+SmjDpeNGzcSAE+dOiV3KQZx7949+vr6MkuWLBw2bFiynsR9+vQpN23axL///puenp7au7EsLCxYunRp9uvXj5s3b5Z1yI0bN26wT58+zJAhAyVJYsWKFbl+/fpk/QJ/+PAh58+fz9q1a9Pa2poAmCVLFrZt25YbNmyINyaYIanVal68eFE7PlvcSAb58+fXyfhsd+/e5YgRI5g7d27a29vT19eXGzdulG10hOjoaAYHB3PGjBls3Lix9tZzAHRycmLjxo05ffp0BgcHJ+tzBwQE0M3NjZaWlvTz8zPKxxL0wcfHhwULFjTqsxejDReVSsX8+fOzSpUqcpeidyqVinPnzqWzszM9PT155swZna8jOjqaZ86cob+/P5s0aaK90wgAs2fPzkaNGnH69Ok8ffq0XrtXIiIiuGLFCpYpU4aSJNHBwYEDBw7Uy6/tmJgYHj16lP3799eOYaVQKFi6dGmOGTOG58+f1+vO+e7dO65bt46tW7dm5syZtYMb1q1blwsXLkzSsyy/EhMTw+3bt7NevXq0t7enm5sbBw8ezJs3b+p8XV968uQJN23axL59+37zY6ZMmTLs378/t2zZopcfMxEREezTpw8lSaKnp2eCznhTulOnThEAN27cKHcpP2S04bJ+/XoCYHBwsNyl6NWdO3dYvXp1ZsmShaNGjTLo3DLPnz/ntm3bOGDAgG+6KUqWLMk+ffpww4YNCeqm+JWrV6+yZ8+etLOzoyRJ9PHx4aZNmwzaTffkyRMuWrSI9evX1w5ImilTJrZs2ZJr16796Si2CaFWq3n27FmOHj2apUqV0j7H5OHhwYEDB/L48eMG/bwPHjzgmDFjmDdvXtrb27N69epcv359srexqKgoBgUFcdq0aWzQoME33bDNmjXjzJkzee7cOYN+3qCgILq7u9PCwoJTpkxJ9WcxVapUYf78+Y32cxpluKhUKubLl4/VqlWTuxS9USqVnDVrFp2cnFi6dGmeP39e7pK0F1hnz57N5s2bfzPBWv369TllypRvLrD+SHh4OJcuXcpSpUpRkiRmyZKFQ4YM4b179wzwaX4uNjaWJ06c4D///MPChQtrx5QqWbIkR44cyTNnziRop33z5g1Xr17NFi1aaJ9TSpcuHRs2bMglS5YYxUi/MTEx3LVrFxs1akR7e3u6urpy4MCBvHHjxi/fG3cDybp169irV694E1/F3UAyaNAgo7mBJDIykv3796dCoeCff/7JkJAQuUvSm+DgYALghg0b5C7lu4wyXNatW0cAPHv2rNyl6MWtW7dYpUoVZs2alWPGjJF11OBfefXqFXfu3Ml//vmHFSpU0I6ga2pqyuLFi7NHjx5cu3Yt79+/rz27uXTpErt168a0adNSoVCwevXq3Lp1q1HPZPn8+XMuW7aMjRo10g4VkjFjRjZr1oyrVq3i69evSf73w+f06dMcPnw4S5QooZ2xs2jRohw8eDBPnjxp1J/z0aNHHDduHPPnz097e3tWqVKFq1ev1t6NGBERwYCAAE6aNIl169ZllixZtD8wcuXKxZYtW3Lu3Lm8ePGiUX/O4OBg5s2bl+bm5pwwYYKsI1DrU7Vq1ZgvXz6jPHsxunBRqVTMmzcva9SoIXcpOhcbG8sZM2Ywe/bsLFeunF7Gv9K3uAnW5s2b980Ea7a2ttoRXDNmzMhBgwYZ5dwuv6JUKhkUFMShQ4eyWLFi2s+XPn16bdehnZ0dmzRpwhUrVhjlHC2/Ehsbyz179tDX15e2tra0tbWlg4ODtivv64mv3rx5I3fJiRYVFcVBgwZRoVCwePHivH79utwl6dzZs2cJgOvWrZO7lG8YXbisWbOGAHju3Dm5S9GpkJAQVq5cmY6Ojhw/fnyKeybhezQaDc+fP8/WrVvT0tJSextx3AE4bjiObt26cdWqVUY5wdr3KJVKBgYGcsiQISxatKg2XDJkyKB9riZ9+vRs3Lgxly9fnmLCJW64ofHjx7NWrVrMlCmT9rPZ29szffr0tLGx4Z9//slly5al6HG4vnT27Fnmz5+fZmZmHDt2rFGfcSVFjRo1mDdvXqM7ezGqcFEqlcydOzd9fX3lLkVnYmNjOXXqVGbPnp1eXl68cuWK3CUlW2hoKOfNm8eiRYtSkiQ6OTlx1KhR2rufEjLB2rhx43jkyBGjOYA9e/aMS5cuZcOGDeN1izVv3pyrV6+O1y0WHBzMESNGxOsWK1KkCAcPHsyAgACjOHjFTXy1YsUKdunS5ZuBUn18fDh8+PB4E18plUoeOHCAzZs3p4ODA52dndmnTx+jfVYoMaKjozlkyBDtD57UsB/GiTt7WbNmjdylxGNU4bJq1SoCMIqL27pw/fp1VqxYkY6Ojpw8ebJRPsCYUBqNhsHBwezQoQOtra1pamrKOnXqcM+ePQn6xRQ3BPrIkSPjDYEeN8Fa586duWzZMoMNgR4bG8vjx49z0KBB9PDwiHdBf9SoUTx79myCL+ivWbMm3gX9tGnTskGDBly8eLFBJgIj/3/iqzFjxrB69erfTPHQoUMHLl68OMETXz1//pxTp05l4cKFaW9vTy8vLy5dulTW2VZ14cKFCyxYsCBNTU05atSoFL1PfsnX15e5c+c2qmtLRhMuSqWS7u7urFWrltylJFtsbCwnT57MbNmysWLFirx27ZrcJSXZx48fOXv2bHp4eFCSJObMmZNjx45N9l1QarWaISEhXLp0KTt27MiCBQtqzwLSp0/PatWqcdSoUTx48GCSptz9nidPnnDhwoWsV6+e9lZkBwcHtmrViuvWreO7d++S/ZnOnTvH0aNH09PTU3umUKhQIQ4YMIDHjh3TycEsru2WLFnCjh07skCBAtq2s7OzY7Vq1Th69GidtJ1KpeLhw4e1z+pkz56dPXr04Llz51Ls2UxMTIx2nnoPDw9eunRJ7pKS7fz58wTA1atXy12KltGEy8qVKwkgRV7k/tLVq1dZoUIFZsuWjVOnTjWKLpLE0mg0DAoKYps2bWhlZUVTU1M2aNCA+/fv12u/bmho6HcnWJMkKUm/vqOjo3nkyBH269ePBQoU0D5EWaZMGY4dO5YXLlzQ+0OU69evZ5s2beI9RFmnTh0uWLAgwQ9R/uisz9ATX718+ZLTp09n0aJFaW9vz3LlynHRokU6C39Du3TpEgsXLkwTExMOGzYsxV8HrVWrFt3d3Y3m7MUowkWpVDJXrlysU6eO3KUkWUxMDCdMmEBHR0dWrlw5Qc8QGJv3799zxowZ2l/Crq6unDBhgmwXrL+cYC2h1w0ePnzIefPmxRv+JWvWrGzXrh03btwo+/Av48ePZ9myZeMN//L333/z8OHDjI6O1l6vWrhwIdu1a/fNxFdx16vknPhKrVbz2LFjbNu2LbNkycJs2bKxe/fuPHPmTIo7m4mJieHo0aNpamrKggULpugu+YsXLxIAV65cKXcpJI0kXJYvX04AKfb09PLlyyxXrhyzZ8/O6dOnp6izFY1Gw4CAALZs2ZKWlpY0MzNj48aNefjwYaMct+jz58/x7nj6coK1uCFHJElisWLFOH78eF6+fNkoD3gfP37k5s2b2bx5c+0ZmkKh0IaOQqFIEXfavX79mv7+/vzjjz9ob2/P0qVLc/78+T+dTdUYXb16lcWKFaOJiQkHDx6cYs9i6tSpw1y5chnF2Yvs4RIbG0tXV1fWrVtX7lISLTo6mmPHjmXWrFnp4+Oj9/GbdOnt27ecNm0a8+bNS0mS6O7uzsmTJ/PVq1dyl/ZL9+7d4+zZs1mjRg3tbc/p06dn/vz56erqqj1A29jY0Nvbm0OGDOGuXbtkf1ZDqVTy0qVLnDdvHlu1ahXvGaEMGTIwf/78dHFx0dafO3du9u7dmwcOHDDosEBJoVarGRAQwA4dOjBr1qx0dHRkly5dGBQUZJSh+D2xsbEcN24czczMmD9//hT5EPelS5cIgMuXL5e7FPnDZenSpQSQ4m4NvHDhAsuUKcPs2bNz1qxZRvFL4VfUajWPHj3Kpk2b0sLCghYWFmzWrBmPHTtm1AeAiIgI7tu3jz179mSuXLkIgGZmZvT29uaUKVN4/fr1ePXHPWU+efJk1q1bV3u9AwDd3NzYsmVLzpkzhxcvXtTr9/b69Wvu2LGD//zzD728vL4Z3aBnz55cu3YtHzx4EK/+T58+cdu2bezUqROzZ8+uHWqlevXqnDVrltEPL//u3TvOmTOHf/75J+3t7VmyZEnOmTMn2TdMGMr169dZvHhxKhQKDhw40KhH0PieunXr0tXVVfYeFFnDJTY2li4uLqxfv76cZSRKVFQUR40axaxZs7JatWpGO3fGl16/fs3JkyfT3d2dkiQxb9689PPzS/ZAjfoS94yGv78/q1atqj07cXZ2ZpcuXbhjx45EXW/42QRradKk0cn4WAkZl+17E18lpPYbN25w6tSprFixorZuNzc39ujRg3v27EnW1Az6FHdjSJcuXejo6MisWbOyQ4cODAgIMMou1y8plUpOnDiR5ubmzJMnT4LmVTIWV65cIQAuW7ZM1jpkDZclS5YQAK9evSpnGQl29uxZli5dmk5OTpw7d65Rn62o1WoeOnSIjRo1opmZGS0tLdmqVSsGBAQY5VlKeHg4d+3axe7du2tnJDQ3N2flypXp5+fHmzdv6rTuyMjIeCP7Ojo6Jmpk3xcvXnDr1q3fjChtZmam8xGlvxQWFsadO3eya9eu2mkTLCwsWKVKFU6fPp23bt0yyu/3/fv3nD9/Pj09PWlvb8/ixYtz5syZsndV/kpISAhLlixJSZL4999/G22Qf61+/fp0cXGR9exFtnCJiYlhzpw52bBhQ7lKSLDIyEgOHz6cWbJkoa+vL+/evSt3ST/04sULTpgwga6urpQkiQUKFKC/v7/RXWDVaDQMCQnhtGnTWLlyZe3FeBcXF3bv3p27d+/WDqZoKD+ak8TS0pIeHh6sUKECS5cuHS+InJyc4s2FY8guFI1Gw1u3bnH69OmsUqUKLSwstOHYtWtX7ty5k2FhYQarJyE0Gg3PnDnD7t2709HRUTuR27Fjx4z2bEalUnHq1Km0sLCgu7s7AwMD5S7pl65evUoAXLJkiWw1yBYuixYtIgCjf8AwODiYJUuWpLOzM+fPn2904/eQ/238+/fvZ/369WlqakorKyu2bduWp06dMqpfsZ8/f+b27dvZpUsX7cyElpaWrFatGv39/fnvv/8aRb1xIdOzZ08WLFhQe4H9y3/29vasWbOmQSZYS6jw8HDu2bOHPXr0oJubm/bsr1KlSpw6dSpv3LhhFO0b58OHD1y0aBHLlStHe3t7Fi1alNOnTzeKofu/5/bt2yxdujQlSWLv3r0N/uMnsRo0aMCcOXPKNgqBLOESExNDZ2dnNmrUSI7VJ0hERASHDBnCzJkzs3bt2kYxB8nXnj17xjFjxjBHjhyUJIkeHh6cM2eO0TzUptFoeO3aNU6ePJne3t7a6wXu7u7s1asX9+3bJ3s3Q1RUFE+dOpXgia/i5oH/2QRrCZ0HXt/u3LnDWbNmsXr16to6nZyc2KlTJ27bts1ohnLRaDQ8d+4ce/TowezZszNz5sxs3bo1Dx8+bHQ/5lQqFadPn04rKyu6ubnxxIkTcpf0Q9euXSMALlq0SJb1yxIuCxcupCRJRvugYVBQEEuUKMEcOXJw8eLFRnW6rlKpuHv3btauXZsmJia0trZmhw4djOYBttDQUG7ZsoUdOnTQHqitrKzo6+vLOXPmyBrSP7uwn9SJr76+kB93vQgAHR0dk3whX9ciIyN54MAB9u7dm7lz59betebl5cVJkybxypUrRrP9LF26lOXLl6e9vT0LFy7MqVOn8vnz53KXFs+dO3dYtmxZAmCPHj2MrvsxTqNGjZgjRw5Zzl4MHi5xZy1NmjQx9Kp/KSwsjIMGDWLmzJlZp04dPnjwQO6StB4/fsxRo0bRycmJkiSxaNGinD9/vuy/PjUaDS9fvswJEyawXLly2i6kvHnzsm/fvjx06JBst3J+fUvylxNffX1Lsi4vfL569SrBtyDL5f79+5w7dy5r1qyprc/R0ZHt27fn5s2bZT/71Wg0vHjxIvv06UNnZ2c6ODiwefPmPHDggNHcSKNWqzlz5kymSZOGLi4uPHr0qNwlfePGjRuUJIkLFy40+LoNHi6rV6+mJElGOf1o37596eLiwmXLlhnV2YpGo6G7uzttbW3ZpUsXnj9/3ih+ZZL/jZ4LgNbW1qxduzbnz59vNBOEbdiwQVubnA9T/ujhyXz58hm0jh+Jjo7m4cOH+ffff2unR+jcubPcZWl9/vyZK1asYMWKFWlvb8/NmzfLXVI89+7do5eXF01MTIxm2/9SkyZNmCtXLoMf0ySSRDIk8+2JIklSol6f2NrUajUAwMTEJFHvA/RfW9zrE7uepLzHWL/TpLZZYteTlNcba5sBqWtbU6lUMDEx0Xtt4vtEkt8TxzTJ7/yf7du3J6uAmJgYmJiYwNT056VoNBo0aNAgUcvet2/fT2tTq9VQqVSwsLBI1HK/V1vNmjUT9Z6ftZtarUZMTAxMTU1hbm6e7NoS227J/U4T4vPnz7CxsUlUbdu3b8fnz5+RLl06PVaW9DYLCwtD2rRp9VTVf5JaW1RUFCRJgqmpKUxNTfXy/SZ1H42OjoalpaXO6/kSyUTto1/vAyqVCkqlEgBgbm6epB+g35PU7/PTp09Ily6dXvfTpNT2pWSHS3BwMCZOnJik9+7evRszZsyAra0tFixYgJw5c/7wtYMGDUr0B71w4QKGDh363b/dvn0bEyZMwLt379CoUSO0bds2yV/UuHHjEh0uZ86cwYQJE7T/nyTu3buHnTt34sSJE3jz5g2srKxQtmxZdOrU6adt8zP//PNPotstOd/p96jVanz8+BGvXr3Cw4cPsW/fPty8eROlSpVKVG1nzpxBQEAAChQogN69eyN//vx62bmS2manTp1C0aJFMXz4cNjb2+u8LiBp+8GZM2dw9OhRSJIEGxsbZM+eHcWKFYOXlxfy588PMzMzndSWlHY7f/48QkJC8Oeff6JPnz56O1iOHTs2UftocHAw3N3d8fLlSzx8+BBPnjzBp0+fQBL29vYoX748WrRoAScnp2TVldTv89ixY8ibNy969OiBP/74w2j2gy8lO1wA/PKs43uCg4PRtGlTzJ49G9evX0e5cuXw5MkTnW3oP6vtwYMHqF+/Plq0aIGmTZuiX79+AIBOnTrpdN0JqU2lUuHSpUuYP38+jhw5gkKFCsHX1xe5cuXCx48fsWXLFpQrVw5TpkxBy5Yt9X5G8WVtyUUSx48fx9y5cxESEgKVSgU7OzsUL14c/v7+2LBhQ6KXOXv2bMybNw9Vq1ZFx44d8c8//8DGxibZterCzJkzMWzYMJQpUwbLli1D+fLlDfZ9/cqkSZMQExODjx8/4v79+zh27BhmzZqFvHnzYsCAAahYsaJstQ4ePBhNmjSBiYkJ+vbtazRttmvXLqRPnx45c+ZE+fLl4eDgAIVCgcePH2PXrl2YN28eJk2ahFatWhm85jlz5mD16tWoU6cOmjZtijFjxuj9jD6xdBIuiaVWq1G1alXMmjULnTp1AkkEBASgU6dOWLFihV7XrVQqUbt2bbRv3x6DBg2CJElwdnZG9erVUbduXWTKlEmv6//S0qVLsXnzZoSEhMDX1xe7du1CoUKF4vUpN2nSBLt27UK7du3w5MkTDBkyxGh2vp8hibFjx8Lf3x/du3dH//794ezsjPTp08PKygqSJCUpXP78808UL14cZ8+eRd++fbFv3z6sXLkSBQsWlL1dSpQogT179mD27NmoVasWJk2ahG7dusleFwD4+Pho/zdJqNVqPH36FCtXrkSLFi1Qp04dTJ8+HdbW1gavrVixYti1axcqV66MIkWKoGLFigav4Xt27Nih7f76+jvs1KmTdr989uwZBg8ebNDvuVSpUihZsiS6dOmCXr16oWzZslizZg08PDyMYnsDAIUcKx01ahTSpUuHzp07Q5IkKBQKHD58GCtXrkRERITe1ksS/fr1Q8aMGbXBAgCFCxdGo0aN0KRJE4NeyDtw4AC8vb0REBCA+fPno2jRot/0h5uYmKBu3bo4fvw4Jk+ejDlz5hi0xqRasWIFJk+ejKNHj2Ls2LHw9PREtmzZkCZNmmRv/AqFAp6enjh27BgqV64MLy8vbNmyxSjaxczMDH379sX27dsxYsQI9O3bV9tXbyzirr24uLhg5MiRCAgIwI0bN1CxYkW8f/9elpry5cuHuXPnok2bNvj48aMsNXwtbl/83vZqamqKevXq4cSJExg/fjwWLVpk8O1PkiR4eHjgwIEDqFWrFry9vY1mPwBkCBe1Wo3x48fj8OHD8b60zJkzw9PTE23atNHbuh89eoTNmzdj69at8dYtSRKmTZuGW7du4enTp3pb/9fWr1+PgQMHwtXV9acHXEmSULRoURw5cgT9+vVDQECAwWpMioiICHTq1An79+9H0aJF9fZLKk2aNJg8eTLmz5+Pjh07YvLkyUaxY0mShEqVKiE4OBgHDhxA3bp1ZTto/4okSciTJw+OHDkCZ2dnlClTRraDe506dVCtWjXUr1/fKL7HX4nbLw8dOoS//voL58+fl6UOS0tLjB8/HgsWLECnTp0wduxY7Z2vcjJ4uPj5+cHBwQF58uT55m87d+7E1q1b9dIwJNGwYUP06NHjuxdbzc3N0aZNG7Ro0ULn6/6RxN61U6JECSxatAi+vr4IDQ3VX2HJ1LhxY5QrVw7lypXT+7okSULjxo1x+PBhzJgxA3379jWKHQsA3N3dcfr0aQD/dWMEBARAo9HIXNX3WVlZYf369ShQoAC8vLwQHR1t8BokScK8efPw+vVr+Pn5pYiAAYDSpUvD398flStX1mvPy89IkoRGjRrh6NGjWLZsGVq1aoWwsDBZaolj0HAhiaFDh2Lnzp3fPaja29sjS5YsmDZtms7XvXHjRoSGhmLw4ME/fM2YMWNw9+5d2b+UH5EkCW3atEG1atXg4+NjlDtfdHQ09u3bhx07dhis71eSJPz55584ffo0du7cifbt20OlUhlk3b+SIUMG7NixAx06dEDDhg3Rvn17XLx40ei6yoD/fuxs2LABtra2qF27tixBaGZmhp07d8LPzw/nzp377mtI4sWLFwgMDMT169dl/zEhSRL++usvlCpVCjVq1JBtv5QkCX/88QeCg4Px/PlzlC9fHrdu3ZKtHoOGS9zG8ueff37375IkYdu2bRg2bJhOGyQyMhL9+/fHqlWroFD8+CObm5ujVKlS6Nmzp87WrWuSJGH9+vW4c+cOFi1aJHc53+jRowcKFSoky50rbm5uOH36NM6ePYumTZsazQHczMwMgwYNQkBAACRJQp06dVCzZk2sX78eHz9+NKofCWZmZjh48CBCQkLwzz//yFKbu7s7pkyZgsaNG8c7OJLE06dPMWTIENSqVQvDhw9HmzZt0L17d9m/a0mSsHPnTly4cAGrVq2StZasWbPi4MGDqFChAsqVK4eNGzfK8j0aNFzq16+P0aNH//QXbalSpQD894yKLpBE69atUapUKZQuXfqXr1+yZAkOHDhgtN0XwH8heODAAfTo0QOfPn2Suxwtkli2bBl2794tWw1Zs2bFqVOncOfOHTRo0ACxsbGy1fIlSZKQP39+LF26FAEBAfD29sbkyZPh6emJOXPmICoqSu4StWxsbBAUFISZM2di7969stTQsmVL/PXXX6hTpw5WrVqFwMBAjBs3Dr6+vnjx4gUWLFiA3bt3Y/v27bh9+za6d+8ue0hbWVlh79696Nixo+w3JVhaWmL69OmYO3cuevbsiT59+hi8q9Ng4RIREYEXL15g4MCBP32dJEkYM2YM6tSpo5ONZdasWbh+/TpWrVqVoG6ajBkzws7ODmvXrk32uvWpVKlS8PX1lfU0/GvHjx+HmZkZnJ2dZa0jY8aMOHnyJJ4+fYq6desiJiZG1nq+pFAo4ObmhkGDBiEoKAhjx47FokWLULFiRdy/f1/u8rRcXFywfv16NGzYEC9fvjT4+iVJwoABAzBlyhRs2bIFw4cPx5MnTzB37lwsW7YMJUqUgK2tLXLkyIEdO3Zg7969OHPmjMHr/JqXlxfq1auHSpUqyb5fxl2PDAoKQlBQEKpUqYJXr14ZbP0GC5fOnTujePHiCXo4b+DAgXj58qXOGmLHjh1IkyZNgl4rSRIWLFig8645XYt7TuT8+fMIDAyUuxwAQLNmzTBp0iSjuM/ezs4OAQEBePPmDWrXrm1UAQNA+7R8o0aNcOrUKRQrVgyenp64fv263KVp1atXD61bt4aXl5cs1zXiuhC3bNmC3bt3Y+HChShXrtw3Q6+kT58e06ZNQ4sWLWTfZyVJwpo1a3Dv3j0sWbJE1lri6smTJw8CAgKQLVs2eHp64tatWwZZt0HChSTWrVuH7du3J+j1JiYmaNOmDapXr57sjaVXr17Ily9fot7j5eUFpVKJe/fuJWvd+mZpaYkFCxagVq1asnfjxcbG4s2bN+jVq5esdXwpbdq0OH78OD5+/AhfX19Z7oBKiLRp02LOnDno2bMnypUrhxcvXshdEoD/Dkzz588HANm6nSRJgoWFBWxtbX96vbRZs2ZQq9XYs2ePAav7vrhu627duuH169dylwPgv67ONWvWoGnTpihbtiwuX76s93UaJFw2b94MGxsbZMuWLcHvWbhwIa5fv46rV68ma91JHQm0U6dOaN26dbLWbQjt2rWDpaUl/Pz8ZK1j/PjxcHZ21tmAfrpia2uLY8eOITw8HNWrV0dkZKTcJX2XJEkYNmwYmjRpgrJlyxrN3W4mJiY4efIkVqxYYRQH7h+Ju425R48esp+9AICnpydat26NChUqyP7DL46JiQkmTJiA/v37o0KFCggJCdHr+vQeLiTRvn17rFixIlEHegsLC0ydOhUVK1bE48eP9Vjh9w0bNgwPHz406udJgP92qoMHD2Lw4MGyXbwmiQkTJmDTpk2yrP9XbGxscPToUWg0GlSqVMmoboL4UtwB0tLSEh07djSKgyQAZMmSBRs2bECjRo3w5s0bucv5oRo1akCpVBrkV/mvSJKERYsWITQ0FCNHjjSa71KSJPzzzz/o16+f3s+S9R4uly5dQnR0NOrXr5/o9/bt2xe1a9dGkyZN9FDZz5mZmaFSpUro0KGDwdedWIULF0a+fPnw119/ybL+169fQ6VS/fAWc2NgbW2NAwcOIEOGDChXrpzRHiRNTExw4sQJrF69GpcuXZK7HK26deuiWbNmqFChguzPlfyIJEkYNGgQ2rRpYxQHc1NTU5w8eRITJkwwqmtpkiRh+PDhaNSoEcqWLau37mK9hgtJ+Pr6YsKECUnunlq2bBm2bt2qh+p+beHChTh16hTevn0ry/oTKu7sZenSpbJ0+zRt2hS1a9c2igv5P2NlZYXt27ejYMGCKF26tNFc2/iag4MD/Pz8jOpBWUmSsHjxYkRHR6NPnz5GU9fXevTogdevXxvN2am7uzsmTpwIb29vo7ktHvj/62mOjo6oW7euXr5PvYbLyZMn8f79e/Tv3z/Jy1AoFIm6VqNLNjY2aNKkCRo1amS0O1OcrFmzokyZMmjVqpVOlvf+/fsE9RVrNBoEBATofTRrXTE3N8fq1atRoUIFlC5d2mjPYHr37g0TExNMnz5d7lK0TE1NERgYiIULF+LIkSNyl/NdJiYm8Pb2RufOneUuRWvAgAHIkSOHUdzN9iWFQoEDBw7g/Pnzerlmq7dw0Wg0qF27NhYsWPDTuzyM3bRp0/DkyRNs3LhR7lJ+Ku4J4e3bt+vk7KVevXoYMmTIL3eGdevWIW3atLCzs0v2Og3FxMQEixYtQvny5VG2bFmjvMgfdzY6cOBA2Z8+/1K2bNmwYsUK1K1b12iHSVq4cCFOnDhhNN13kiTh6NGj2LFjh9GFctz1yH/++Qd3797V6bL1ctQniSFDhiBt2rRo3769PlZhMGZmZli7di369+9vsPvDkypDhgwoXbq0Ts5eVqxYgenTp//0DiGS6Ny5M1avXm30XWJfUygUWL58OZycnHRyy7s+FC1aFLly5ULfvn3lLiWeZs2aoVKlSqhatapRtlu6dOng4OCAuXPnyl2KVvr06bFq1SrUqVPH6J65Kly4MIYOHarz55n0Ei4XLlzA1KlTtWMppXSlSpVC//79Ua9ePZ2nu67Fnb0kdwN2dXXFhg0b0LBhQzx58uS7rzl//jxiY2NRq1atZK1LLiYmJtizZw/u3LmDUaNGGd2BUpIkHDp0CHPnzjWqsxdJkrBp0yaEhIRg8eLFcpfzDUmSsGrVKkyaNMmovtOmTZuiYMGCaN68uVHVJUkSRo4cCQsLCwwYMEBny9V5uDx8+BCVKlWCv78/XF1ddb14WUiShN69e6NVq1aoXbs2Tpw4YVQbx5cyZsyIggUL6mTwzXr16qF79+4oU6bMN10gJFGjRg1MmzYtRf+AsLKyQkBAAMaNG2eUD806OzsjT548+Pvvv+UuJR5LS0vs378ff/31l1HOVVO0aFGYmZnhwIEDcpeiFfdjYceOHbhx44bc5cSjUCgQEBCAmTNn4tGjR7pZpk6Wgv8ONmfOnIGnpyfatWuHHj166GrRRkGSJAwZMgQDBw5Ely5dMGHCBISHh8td1nft3bsXS5cuTfbDW5Ikwc/PDwUKFEDFihXx4cMHAP99135+ftBoNEb1RH5S5c6dG0OHDoW3t7fR/WiQJAn79+/H3LlzjeZhvDienp5o3LgxKleubJTtNmvWLHTr1s2oarOzs8P48eONss2cnZ3Rp08fVKxYUSe16SRcDhw4gO7du8PX1xc9e/bEjBkzUvSv2R+RJAlt27bFpk2bEBQUhFq1aiEoKEjusr6RPXt2ZMqUSSd3GikUCuzcuRMODg7w9PTEkiVLMHr0aIwYMQLHjx9P0TdrfGnUqFEICwvD8uXL5S7lGzlz5tTZ96lLkiRhxYoVuHv3LjZs2CB3Od+Iuz1+8+bNcpcSz8CBAxEVFWWU29qUKVPw9u1brFmzJtnL+vUokgkwfPhw5M2bF7t370axYsWM6n5ufTwglCdPHqxfvx5LlizBrFmzkD9//iQtR59jXW3atAnTpk1D7ty5k/T+r2vbuHEjFi5ciJUrV8La2hp79uxBnjx5DD5el77bbP78+ciVK1eS3p+Svk9d2rBhA5YuXQo3N7ckvV+ftS1ZsgSrVq1Czpw5E/1efda1efNmzJs3z2i3tUWLFiX5+4wjMZnnP/v27cPnz59hZWWl17MVExMT+Pr6Juo9R44cSdTdDxqNBhqNJkEjN8eJiYlBmjRpULly5UTVtm/fPr2PH6VWq2Fubp7odvtZbUqlEgqFQidjiCX2O02pbaYrqbG2I0eOGKw2Hx+fBL/HmNvMmGv7UrLDxZD9hokNr8TW9vnzZ8TGxiJdunQwMzNL1Hv1XduXr0/suvRdW3IkpraE1vXlzIVx6/hd2wxIXG0kjbrdSEKtVsPExESvtaWG7/Pr/SApXdjJOWFIdod53AaY0H8ksXnzZhQqVAgKhQJVq1bF6dOnE/RefdcG/DcDnoeHB27cuJHo9+qztitXrsDU1BRXrlxJ0ufSR20rVqyAiYkJunbtCpKJrispB4ef/dNoNFi3bh0KFCgAExMT1K5dGxcuXIBCoTCaNov7FxERgalTp8LBwQEWFhbo0qULHj9+LHttCoUCN27cQObMmVGiRAl8/PjRqNrtxo0bcHR0TPT+qettLe4fSXTs2BEmJiZYs2aN3veBhNQWFhaGCRMmIFOmTLCyskKvXr3w4sULg9QWD2WiVqu5adMmFixYkABYuXJlBgYGylWOVmhoKKtWrcrcuXPz2rVrcpejdfHiRUqSxIsXL8pdCkly6dKllCSJXbt2pVqtlrUWpVLJ1atXM3fu3ARAX19fnj17VtaaEiosLIxTpkxhpkyZaGpqyo4dO/LBgwdyl8WrV6/S3t6eRYsW5fv37+UuRyuurqtXr8pdCtVqNdu1a0eFQsHVq1fLXQ5DQ0M5duxYpk+fnubm5vzrr7/49OlT2eqRLVziqNVqbtmyhR4eHgTAihUrMiAgQNaaPn36xGrVqjF37txGsRGTxhUuixcvJgB269aNGo1GtjqUSiVXrlxJd3d3AmCtWrV4/vx52epJjvDwcE6bNo0ODg40NTVl+/btef/+fVlrunbtGu3t7VmkSBG+e/dO1lriGEu4qFQqtm3blgqFgmvXrpW1ltDQUI4ePZp2dna0sLBgz549+ezZM1lrIo0gXOKo1Wpu27aNhQsXJgBWqFCBx48fl62eT58+sXr16sydOzevXLkiWx1xjCVcFi5cSAD866+/ZAsWpVLJ5cuXM1euXATAOnXqyN4uuhIREcHp06czc+bMNDExYdu2bXn37l3Z6rl+/TozZcrEwoUL8+3bt7LVEccYwkWlUrF169ZUKBRct26dbHV8/PiRI0eOZLp06WhpaclevXrx+fPnstXzNaMJlzhqtZrbt29n0aJFCYBeXl48duyYLAeyz58/09fXl+7u7rx8+bLB1/8lYwiXBQsWEAB79uwpy/cRGxvLZcuW0dXVlQBYt25dXrp0yeB1GEJERARnzJjBLFmy0MTEhG3atOGdO3dkqeXGjRt0cHCgh4eH7AEjd7ioVCq2atWKJiYm3LBhgyw1fPjwgSNGjNCGSp8+ffjixQtZavkZowuXOBqNhjt37mSxYsUIgOXKlePRo0cNflD7/Pkza9asSXd3d1kPZHKHy/z58wmAvXr1Mvh3EBsbyyVLltDFxYUAWL9+faM4mzSEyMhIzpw5k1mzZqVCoWCrVq3477//GryOkJAQOjg4sFChQnzz5o3B1x9HznBRqVRs0aIFTUxMuHHjRoOv//379xw2bBjTpk1LKysr/v3333z58qXB60goow2XOBqNhrt37+Yff/xBACxbtiwPHz5s0ANcWFgYa9WqxVy5csl2cJczXObOnUsA7N27t0HbPSYmhosWLWLOnDkJgA0bNpS9r10uUVFRnD17NrNly0aFQsEWLVrw1q1bBq0hJCSEmTNnZsGCBfn69WuDrjuOXOGiVCrZvHlzmpiYcNOmTQZd97t37zh06FDa2trSysqK/fr146tXrwxaQ1IYfbjE0Wg03LNnD0uUKEEALF26NA8ePGiwg11YWBhr165NNzc3XrhwwSDr/JJc4TJnzhwCYN++fQ3W1jExMVy4cCFz5MhBSZLYqFEjo7pzT05RUVGcM2cOs2fPTkmS2Lx5c968edNg67916xazZMnCAgUKyBIwcoSLUqlk06ZNaWpqyi1bthhsvW/fvuXgwYNpY2PDNGnScMCAAbKFelKkmHCJo9FouG/fPpYsWZIAWKpUKR44cMAgB77w8HBtwBj6riQ5wmXWrFkEwH79+hmkfaOjozl//nw6OztTkiQ2adKEN27c0Pt6U6Lo6GjOmzePTk5OlCSJTZs2ZUhIiEHWHRcw+fPnN/gvaEOHi1KpZJMmTWhqasqtW7caZJ1v3rzhoEGDaG1tTWtraw4aNEjWrsikSnHhEkej0fDAgQMsVaoUAbBkyZLct2+f3g+C4eHhrFOnDl1dXQ36LIWhw8Xf358A2L9/f7236dcHymbNmhnsQJnSRUdHc8GCBQYP5Nu3bzNr1qzMly+fQfv9DRkusbGxbNSoEU1NTblt2za9r+/NmzccOHAgra2taWNjw3/++Uf2GyiSI8WGSxyNRsODBw+ydOnSBMA///yTe/bs0esBMSIigvXq1aOrqyvPnDmjt/V8yZDhMmPGDALgwIED9dqOX3bxKBQKg3fxpCZydCX++++/dHR0ZN68eQ0WMIYKl9jYWDZs2JBmZmbcsWOHXtf1+vVr9u/fn2nSpKGtrS2HDBliNM8VJUeKD5c4Go2Ghw8fZtmyZQmAxYsX5+7du/V2cIyIiGD9+vXp4uJikIAxVLhMnz6dAPjPP//ore2ioqI4a9YsOjo6UqFQsGXLlrx9+7Ze1vW7iYmJ4eLFi7U3QTRo0ECvB+I7d+4wW7ZszJs3r0FuhzVEuMTGxrJBgwY0MzPjzp079baely9f8u+//6aVlRVtbW05bNgwoxoNIblSTbjE0Wg0PHr0KMuVK0cA/OOPP7hz5069HCgjIyPZoEEDuri4MDg4WOfL/5IhwmXatGkEwMGDB+utvWbOnKkNldatW8tyW+3vIDY2lkuXLjXI7dt3795l9uzZmTt3br0/xKfvcImJiWG9evVoZmbGXbt26WUdL1++ZN++fWllZcW0adNy+PDhqSpU4qS6cImj0Wh47Ngxenl5EQCLFi3K7du36/ygGRkZyYYNGzJnzpw8ffq0Tpf9JX2Hy5QpUwiAQ4cO1UsbGcsDgb+buAdP3dzc9Prg6b179+jk5KT3gNFnuMTExLBu3bo0Nzfn7t27db78Fy9esHfv3rS0tGS6dOk4cuRIfvjwQefrMRapNly+dOLECXp7exMACxcuzG3btul0sMWoqCg2atSIOXPm5KlTp3S23C/pM1wmT55MABw+fLhOgyUiIoJ+fn7aoUzatWvHe/fu6Wz5QsIplUquWLFCO2RO7dq1db4t3b9/n05OTnR3d9fb2Fb6CpeYmBjWqVOH5ubm3Lt3r06X/ezZM/bs2ZMWFha0s7Pj6NGj+fHjR52uwxj9FuESJyAggBUrViQAenh4cMuWLToLmaioKDZu3Jg5cuTQy+jO+gqXiRMnEgBHjBihs2D5ehDGDh06yD4Io/AfpVLJVatWxRvsU5fPbd2/f5/Ozs7MlSuXXkbk1Ue4REdHs1atWrSwsOC+fft0ttxnz56xR48etLCwYPr06TlmzBiGhobqbPnG7rcKlziBgYGsXLkyAbBQoULctGmTTkImKiqKTZs2ZY4cOXjy5EkdVPr/9BEu48ePJwCOGjVKJ8sLDw83yuHjhW/FTVOQJ08e7TQF586d08myHzx4wBw5ctDNzY1PnjzRyTLj6DpcoqOjWbNmTVpYWHD//v06WeaTJ0/YvXt3mpubM0OGDBw3bhw/ffqkk2WnJL9luMQ5deoUq1SpQgAsUKAAN27cmOyQiY6OZrNmzejs7KzTqQN0HS7jxo0jAI4ePTrZywoLC+OkSZNob29PMzMzdu7cmQ8fPkx+kYLeqVQqrl27lnnz5iUAVq9eXSd3Pz58+JA5c+akq6srHz9+rINK/6PLcImOjqavry8tLCx44MCBZC/v8ePH7NatG83NzZkxY0ZOmDCBnz9/TvZyU6rfOlzinD59mlWrViUA5s+fn+vXr6dKpUry8r4MmBMnTuikRl2Gy5gxYwiAY8aMSdZyPn/+zIkTJzJjxow0MzNj165d+ejRo2TXJxieSqXi+vXrmS9fPgJgtWrVkn0H5KNHj5gzZ066uLjobLvQVbhERUWxRo0atLS05MGDB5O1rEePHrFLly40MzNjxowZOXHixN86VOKIcPlCcHAwq1evTgDMly8f165dm+SQiYmJYYsWLejk5KSTeWl0FS6jRo0iAI4bNy7Jy/j06RPHjx/PDBky0NzcnN26ddPpr1NBPiqVihs2bGCBAgUIgFWqVEnWTSqPHz+mi4sLc+bMqZOA0UW4REVFsVq1arS0tOThw4eTvJyHDx+yU6dONDMzo729PSdPnsywsLAkLy+1EeHyHWfPnqWvry8BME+ePFyzZk2SQiYmJoYtW7akk5MTjx07lqyadBEuI0eOJABOmDAhSe//9OmTUU2jKuiPLqchf/LkCV1dXZkzZ85kd5cmN1yioqJYtWpVWllZ8ciRI0laxoMHD9ixY0eamprSwcGBU6dOZXh4eJKWlZqJcPmJc+fOsWbNmgTA3Llzc9WqVVQqlYlaRkxMDFu1akUnJycePXo0ybUkJ1w0Gg1HjBhBAJw4cWKi3x8aGsoxY8Ywffr0tLCwYI8ePUSo/CbipiEvVKgQAbBSpUpJulnlyZMndHNzY44cOZJ1k0dywiUyMpJVqlShlZVVkvbF+/fvs3379tpQmTZtmgiVnxDhkgAXLlxg7dq1CYDu7u5csWJFokImNjaWbdq0Yfbs2ZP8aymp4aLRaDhs2DAC4OTJkxP13o8fP3LUqFG0s7MzymlUBcNRq9XcunWrdhpyb2/vRF9PfPr0KXPlykVnZ+ck35qe1HCJjIykj48P06RJk+hu6rt377Jt27Y0MTFhlixZOH36dEZERCRqGb8jES6JcOnSJdatW5cA6ObmxuXLlyc4ZGJjY9m2bVtmz549Sf28SQkXjUbDoUOHEgCnTp2a4PellGlUBcOLm4a8SJEi2mnIE3OwfvbsGd3d3enk5JSkgElKuERERLBy5cpMkyZNogLxzp07bNOmDU1MTJg1a1b6+/szMjIy0TX/rkS4JMHly5dZr149AqCrqyuXLl3K2NjYX74vNjaW7dq1Y/bs2RN9h0piw0Wj0XDw4MEEwGnTpiXoPe/fv+fw4cO106j27dvXqKdRFeQTNw150aJFCYDly5dP8DTkz549Y+7cuZk9e/ZEj9iQ2HCJiIhgxYoVaW1tneBHA/7991+2atWKCoWCWbNm5cyZM0WoJIEIl2S4cuUKGzRoQAB0cXHh4sWLfxkysbGx7NChA7Nnz56oe+sTEy4ajYaDBg0iAE6fPv2Xr0+p06gK8tNoNNy1a1eipyF//vw58+TJw2zZsvHu3bsJXl9iwiU8PJze3t60trZO0HWiW7dusUWLFlQoFMyWLRtnz57NqKioBNcmxCfCRQeuXbvGRo0aEQBz5MjBRYsWMSYm5oev/zJgEvpUcELDRaPRcODAgQTAGTNm/PS1KX0aVcF4fG8a8kOHDv00ZF68eMG8efMyW7ZsCR7INKHhEh4ezgoVKtDGxuaXd7ndvHmTzZs3pyRJzJ49O+fOnStCRQdEuOjQ9evX2bhxY0qSRGdnZy5YsOCHIRMbG8uOHTsyW7ZsCRooLyHhotFo2L9/fwLgzJkzf/i6t2/f8p9//qGNjQ2tra05cODAFDmNqmB84qYh//PPPwmAnp6eP52G/OXLl8ybNy8dHR0TNP1CQsIlLCyM5cuXp42NDYOCgn74upCQEDZt2pSSJNHJyYnz5s1jdHT0rz+kkCAiXPTgxo0bCdpolUolO3fuzGzZsnHPnj0/XeavwkWj0fDvv/8mAM6ePfu7r0lt06gKxkuj0XD//v0Jmob81atXzJ8/P7NmzfrLSeN+FS5hYWEsV64cbW1tf/jw5/d+BIpQ0T0RLnr0vdPtrzdipVLJLl26MFu2bD+dQ+Jn4aLRaNi3b18C4Jw5c775+5fTqNrY2KSaaVQF4/e9acj37t37Tch8GTC3bt364fJ+Fi6fP39m2bJlaWtr+925lRLbfS0kjwgXA/jVhUKlUsmuXbvS0dHxu7PfaTQaHjlyhJIk8ciRI/F2TI1Gw969exMA586dG+99r169Yr9+/bRzcw8dOlSEiiCLuGnIy5Qp88NpyF+/fs0CBQowS5YsvHnz5neXceLECWbIkIEnTpyI997Pnz+zTJkyTJs27Tdjol29elV7403OnDm5ePFiESoGIMLFgG7fvq29xdHR0THeLY5KpZLdu3eno6Ojdt7ujx8/0t/fXzuLYNw/Nzc3+vv788OHD+zVqxcBcP78+dr1/C7TqAopT9wPpR9NQ/7mzRsWKlSImTNnZkhICMlf7wePHz9m6dKlmS5dOp49e1a7ri8fGXBxcUnwIwOCbohwkcG///7L1q1bf/NwlkqlYo8ePejo6MiRI0fS2tqakiRRkqR4O1Xc/zc1NSUALly4kOTvN42qkHJ9bxryHTt2UKPR8M2bN/Tw8KCDgwMXLlz4y/1AoVDQ2tpaOx/N1w87L1u2TISKDES4yOh7w0p8/vxZO9TM1zvT9/5JksS1a9eyV69etLS0pJ2dHUeNGvVbTKMqpA7Hjx9nhQoVCIBFihThtm3b+Pr1a7q6uiZ4P1AoFJw9e7Z238mVK1eih2kSdEuEixG4d+8e27dvTxMTEzo4ONDMzOyXO9PX/9KlS/fbTaMqpC5fTkNeoEABmpubJ3o/cHNzS9IAs4LuSSQJwSg8ePAALVq0wJkzZxL93kmTJmHQoEF6qEoQDCswMBAdO3bEnTt3Ev3e6dOno2/fvnqoSkgsES5GhCTc3d1x//79RL1PkiS4urri7t27kCRJT9UJgmGI/SB1EOFiRN69e4dMmTIl6/0ZM2bUYUWCYHhiP0gdFHIXIPy/8PDwZL0/LCxMR5UIgnzEfpA6iHAxIjY2Nsl6v62trY4qEQT5iP0gdRDhYkQyZswINze3RPcXS5IENzc3ZMiQQU+VCYLhiP0gdRDhYkQkSULPnj2T9N5evXqJi5hCqiD2g9RBXNA3MqGhociePTuioqKg0Wh++XqFQgErKys8e/YMdnZ2+i9QEAxA7AcpnzhzMTJ2dnbYunUrJEmCQvHzr0ehUECSJGzbtk3sUEKqIvaDlE+EixGqWrUq9u7dCysrK0iS9M1pftx/s7Kywr59+1ClShWZKhUE/RH7QcomwsVIVa1aFc+ePYO/vz9cXV3j/c3V1RX+/v54/vy52KGEVE3sBymXuOaSApDEhw8fEBYWBltbW2TIkEFctBR+O2I/SFlEuAiCIAg6J7rFBEEQBJ0T4SIIgiDonAgXQRAEQedEuAiCIAg6J8JFEARB0DkRLoIgCILOiXARBEEQdE6EiyAIgqBzIlwEQRAEnRPhIgiCIOicCBdBEARB50S4CIIgCDonwkUQBEHQOREugiAIgs79H5GuboyB4z4oAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 500x400 with 22 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot KAN at initialization\n",
    "model(dataset['train_input']);\n",
    "model.plot(beta=100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "8071b133",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 500x400 with 22 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# if you want to add variable names and title\n",
    "model.plot(beta=100, in_vars=[r'$\\alpha$', 'x'], out_vars=['y'], title = 'My KAN')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ddf67e30",
   "metadata": {},
   "source": [
    "Train KAN with sparsity regularization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "97111d75",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "| train_loss: 5.20e-02 | test_loss: 5.35e-02 | reg: 4.93e+00 | : 100%|█| 20/20 [00:03<00:00,  5.22it"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "saving model version 0.1\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "# train the model\n",
    "model.fit(dataset, opt=\"LBFGS\", steps=20, lamb=0.01);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2f30c3ab",
   "metadata": {},
   "source": [
    "$\\beta$ controls the transparency of activations. Larger $\\beta$ => more activation functions show up. We usually want to set a proper beta such that only important connections are visually significant. transparency is set to be ${\\rm tanh}(\\beta \\phi)$ where $\\phi$ is the scale of the activation function (metric='forward_u'), normalized scale (metric='forward_n') or the feature attribution score (metric='backward'). By default $\\beta=3$ and metric='backward'."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "3f95fcdd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 500x400 with 22 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model.plot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "6383a22f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 500x400 with 22 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model.plot(beta=100000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "cbd0f521",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 500x400 with 22 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model.plot(beta=0.1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d0925b09",
   "metadata": {},
   "source": [
    "plotting with different metrics: 'forward_n', 'forward_u', 'backward'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "34fe7629",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 500x400 with 22 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model.plot(metric='forward_n', beta=100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "e92f7c7a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 500x400 with 22 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model.plot(metric='forward_u', beta=100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "68e99753",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 500x400 with 22 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model.plot(metric='backward', beta=100)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9e788b91",
   "metadata": {},
   "source": [
    "Remove insignificant neurons"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "ed4800ea",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "saving model version 0.2\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 500x400 with 6 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model = model.prune()\n",
    "model.plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "61c8eeb1",
   "metadata": {},
   "source": [
    "Resize the figure using the \"scale\" parameter. By default: 0.5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "5cb8d57e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 500x400 with 6 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model.plot(scale=0.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "67305f39",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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CYII=",
      "text/plain": [
       "<Figure size 200x160 with 6 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model.plot(scale=0.2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "51c722ad",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 2000x1600 with 6 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model.plot(scale=2.0)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "03d4bf1b",
   "metadata": {},
   "source": [
    "If you want to see sample distribution in addition to the line, set \"sample=True\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "c6d24148",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 500x400 with 6 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model.plot(sample=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a3fa482a",
   "metadata": {},
   "source": [
    "The samples are more visible if we use a smaller number of samples"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "3856bcb6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 500x400 with 6 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model.get_act(dataset['train_input'][:20])\n",
    "model.plot(sample=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4fa7ca2c",
   "metadata": {},
   "source": [
    "If a function is set to be symbolic, it becomes red"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "3d502880",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "r2 is 0.9992202520370483\n",
      "saving model version 0.3\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "tensor(0.9992, device='cuda:0')"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.fix_symbolic(0,1,0,'x^2')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "f8f93b9c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 500x400 with 6 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model.plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e75a0760",
   "metadata": {},
   "source": [
    "If a function is set to be both symbolic and numeric (its output is the addition of symbolic and spline), then it shows up in purple"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "17df5fed",
   "metadata": {},
   "outputs": [],
   "source": [
    "model.set_mode(0,1,0,mode='ns')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "b5b13363",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 500x400 with 6 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model.plot(beta=100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "628e9c8a",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.16"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
